Generating Statistical Distributions using Fractional Differential Equations

Abstract

In a recent paper of Dixit and Ujlayan (UD), a new fractional derivative is introduced as a convex combination of the function and its first derivative; that is Dα f(x) = (1 − α)f(x) + αf′(x). In this article, a new technique of generating fractional continuous probability distributions by solving UD fractional differential equations that associated to well-known continuous probability distributions is presented. In particular, the UD fractional probability distributions for the Exponential, Pareto, Lomax, and Levy distributions are generated. Finally, a real data application is considered for investigating the usefulness of the new fractional distributions. The results reveal that the pro posed new fractional distribution performs better than the baseline distribution.